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For mathematical induction proofs, it is very important to follow through each step carefully, and our first step should be to test the condition. so we are asked to prove for all positive integers, so can you write out the test for a positive integer for step 1?

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Cus like our teacher was quite strict on following the correct setup and all

anonymous

2 years ago

YES IT DOES BUT I WAS LIKE CHANGING THE OAGE AND SAW ALL THAT I WAS LIKE WTH WHERE DID THAT COME FROM HAHA

anonymous

2 years ago

PAGE

FireKat97

2 years ago

hahaahahhaa

anonymous

2 years ago

ok so go on

FireKat97

2 years ago

okay so after you test for your first step, you want to let n = k for your second step (another useless convention I suppose but it was necessary for us)
so its like...
Step 2, for n = k
8 + 16 + 24 + ... + 8k = 4k(k + 1)

anonymous

2 years ago

wait what was step one again haha sorry

FireKat97

2 years ago

hahah no problem, step 1 is to test the condition

FireKat97

2 years ago

so because we are asked to prove for all positive integers, its easiest to test for n =1

anonymous

2 years ago

ok how do i do that agin hah im sorry i was at base untill 8pm cuz my comander is an retriceso im very sleepy and slow haha

FireKat97

2 years ago

haha no problem, so you can test this by saying;
test for n = 1
and then sub n = 1 into both the left and right hand sides and show that they are equal

anonymous

2 years ago

ok so it would look like umm shiz hah i for got ho to write it haha i jsut ad it sorry

so we can make the LHS look like the RHS through factoring out the x + 1

anonymous

2 years ago

this is why this is my last class and im done with school haha

FireKat97

2 years ago

hahahahaha well school isn't that bad

FireKat97

2 years ago

I used to hate it, but you miss it once you leave

FireKat97

2 years ago

well I'm told I should be missing it but meh

anonymous

2 years ago

i will never haha

FireKat97

2 years ago

haha you never know

FireKat97

2 years ago

anyway so once we get the LHS to look like the RHS we can move onto step 3

anonymous

2 years ago

ok i really need to go to my next problem so wnot to be rood but whats next mate ahah

FireKat97

2 years ago

and for step 3, we just need to kind of sum stuff up and say that by the law of mathematical induction.. blah blah blah (Im pretty sure you can google one of these statements, i don't remember them exactly) we have proven that the above statement is true for all positive integers

FireKat97

2 years ago

but yea just make sure you write up the proof with all your steps in a formal way in a test

anonymous

2 years ago

hat should i exactly google

FireKat97

2 years ago

its actually just something along the lines of "According to the Principle of Mathematical Induction P(n) is true for any positive integer, as proven above"

FireKat97

2 years ago

and thats your final step

anonymous

2 years ago

thnx on two my next headache haha

FireKat97

2 years ago

haha no problem :) Just post them up and Ill try and take a look a bit later